GENERALIZED ROPER-SUFFRIDGE OPERATOR FORϵSTARLIKE AND BOUNDARY STARLIKE MAPPINGS

摘要

This article is devoted to a deep study of the Roper-Suffridge extension operator with special geometric properties.First,we prove that the Roper-Suffridge extension operator preservesϵstarlikeness on the open unit ball of a complex Banach space C×X,where X is a complex Banach space.This result includes many known results.Secondly,by introducing a new class of almost boundary starlike mappings of orderαon the unit ball B n of C n,we prove that the Roper-Suffridge extension operator preserves almost boundary starlikeness of orderαon B n.Finally,we propose some problems.